The role of patterning within and beyond mathematical thinking

This thesis is a theoretical inquiry into the construct of pattern across fields of knowledge to highlight elements of patterning that are intrinsically similar. In the first stage of this inquiry, a comparison of pattern recognition, a neuropsychological construct based on the work of Goldberg (2005), and pattern as defined in the field of mathematics education, generated a tentative generalised model of patterning (McCluskey, Mitchelmore, & Mulligan, 2013). This model was proposed to describe the nature of patterning across both domains of knowledge. A subsequent analysis of patterning across broader fields of cognitive neuroscience and the psychology of mathematics education supported a more generalised view of patterning within and beyond mathematical thinking. In mathematics education, generalisations about concepts are formed through identification of patterns and relationships and the capacity to reason. Therefore in the next stage of this research I undertook a content analysis of key terms to highlight the incidence of the proficiency-reasoning developed throughout the Australian Curriculum: Mathematics. A dynamic view of the role of reasoning within the proficiencies, connected with the authors' initial generalised model of patterning (McCluskey, Mitchelmore, & Mulligan, 2013) is therefore proposed to support the further development of generalised understandings in mathematics education.